I see no certainty that a prolonged effort to reassert total Suni control will take place. There may be some effort but when they secure the natural Suni tribal areas, the effort will diminish
Their main task is going to be learning how to governwhat they have.
They are not going to stop until they gain the riches in the North and South (oil) or the riches in Baghdad. The land they control now is mostly impoverished.